Summary: In this work, an unconditionally stable method using the associated Hermite (AH) orthogonal functions for solving the convection-diffusion equation is proposed. The time derivatives in the equation are expanded by the weighted Hermite functions. By introducing the Galerkin temporal testing procedure to the expanded equation, the time variable can be eliminated in the process of calculation. An implicit difference equation can then be obtained in AH domain under no convergent conditions. The numerical results of the equation can be obtained by solving the expanded coefficients in AH domain recursively. Two numerical examples are conducted to validate the accuracy and the efficiency of the proposed method by comparing to the conventional finite difference method and the alternating direction implicit (ADI) method. The numerical results show that the accuracy of this unconditionally stable method is independent of the time step size, and this proposed method has great advantage in efficiency in a computational domain with fine structure in convection-diffusion problems. Moreover, the agreement between the results obtained using the FD method and the proposed method is very good.